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A polynomial with two terms
The number that corresponds to a point on a number line
the number in front of the variable
the coordinate (0,0)
A mathematical sentence that shows the relationship between quantities that are not equivalent
A mathematical phrase without an equal sign.
To find the value of a mathematical expression.
2nd degree
A mathematical sentence that contains an equals sign
One of two numbers whose product is 1; it is also called multiplicative inverse.
The process used to find the value or values that make an equation true.
The point where two sides meet. (Shared end points of the line segments of a polygon.)
Axis of Symmetry
a line that divides a parabola in two equal halves and goes through the vertex
the solutions to a quadratic equation
A relationship that graphs as a straight line. This means y is changing at a constant enterval.
Quadratic standard form
y = ax² + bx + c
Greatest Common Factor
Difference of 2 squares
M/C Chart
factoring the trinomial by using the multiplacation number and the combine number
Factor Completely
factoring by using at least 2 different methods
leading coefficient
The coefficient of the term with the highest degree
the decimal part
quadratic equation
ax² + bx + c = 0
A plane figure that can be folded along a line so the two parts match.
Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Parent Function
the most basic function of a family of functions, or the original function before a transformation is applied
Minimum Value
The lowest point of a parabola (when a>0)
Maximum Value
The highest point of a parabola ( when a<0)
Intercept Form
the point where the line crosses the x-axis
Square Root
when multiplying a number by itself to get a square number
Zero Of a Function
a value of x that makes the function's value zero
Perfect Square
the number that forms when two same numbers are multiplied together
Linear Function
y = mx + b
Exponential Function
y = ab^x
Axis of symmetry (mathematically)
X = - b/2a
the graph of a quadratic function
domain of parabola
all real numbers
translate or shift
move up or down
wide parabola
small coefficient of X
narrow parabola
large coefficient of X
the lowest possible y value for the graph of a quadratic function; also the y -coordinate of the vertex
the highest possible y value for the graph of a quadratic function; also the y-coordinate of the vertex
The axis of symmetry. Also, the line that goes through the center of a parabola.
standard form
y = ax^2 + bx + c
The ______________________ is all the possible INPUT, X, values.
The difference between the greatest number and the least number in a set of data.
vertex form
y = a(x - h)^2 + k
intercept form
y= a(x - p)(x - q)
A number, a variable, or the product of a number and a variable
A polynomial with 3 terms
the point where the line crosses the y-axis
the point on a graph where y = 0, also points where the graph crosses the x-axis
methods for solving
factoring, square root method, completing the square, quadratic formula and graphing
imaginary number, the square root of -1
i squared
complex number
includes real and imaginary numbers
f(x) = -2(x-3)(x+5). Axis of symmetry is
f(x) = x²-5x+3. Axis of symmetry is
f(x) = -3(x+4)²-5. Range is
f(x) ≥-1
f(x) = x²+2x. Range is
(0, 9)
f(x)= -¾(x+4)(x-3). y-intercept is
(0, -2.5)
f(x)=½(x-1)²-3. y-intercept is
-2, -6, -10, -14, ...
f(x)=-2x²-4x+9. First differences from vertex are....
1/4, 3/4, 5/4, 7/4, ...
f(x)=¼(x+7)²-2. First differences from vertex are...
f(x)=5(x-7)(x+2). x-intercepts are
(7, 0) and (-2, 0)
(8, 0) and (2, 0)
f(x) = (x-5)²-9. x-intercepts are
(11, 12)
Axis of symmetry is x=5 and point (-1, 12) is on the graph. Another point is
(-11, 0)
Vertex is (-4, 13) and x-intercept is (3, 0). The other x-intercept is
FOIL, distribute and combine like terms
To convert Vertex Form to Standard Form you must
To convert Factored Form to Vertex Form you must
Average the x-intercepts and plug that number in to find the vertex. Keep the leading coefficient.
To convert Factored Form to Standard Form you must
To convert Standard Form to Vertex Form you must
Find -b/2a and plug that number in to find the vertex. Keep the leading coefficient.
To find the x-intercepts with Standard Form you must
Re-write into Factored Form by factoring, or use the Quadratic Formula
To find the leading coefficient if you know the x-intercepts and another point.
Write a Factored Form equation with the x-intercepts and solve for 'a' with the other point.
Write in Vertex Form and solve for 'a' with the other point.
To find the leading coefficient if you know the vertex and another point.
The second differences are constant and equal to 2a (twice leading coefficient)
What is always true about the 2nd differences for a quadratic equation?
Maximum because a≤0
f(x)=3+2x-x² has a minimim or maximum point?
How do you factor f(x)=-x²-4x+12?
How do you factor f(x)=-3x²+5x?
<0 (no answers), =0 (1 answer), >0 (2 answers)
What does the value of the discriminant tell you?
f(x)= (3x-4)(3x+4)
How do you factor f(x) = 9x²-16?
f(x)= (5x-1)(x+3)
How do you factor f(x) = 5x²+14x-3?
Leading coefficient = -3. How do you plot points starting at the vertex?
Over 1 each way and down 3, then over 1 each way and down 9, then over 1 each way and down 15, etc.
Minus 2 from both sides. Square both sides. Minus 3 from both sides.
How do you find the quadratic equation that has solutions of x = 2 ±√3?
How do you solve 3x²=4x-11?
Make one side = 0. Try to factor, or find a, b, c and use the Quadratic Formula
How do you simplify (8±√28)/6?
x ≈ 1 and x ≈ -9.
The x-intercepts are x=-4±√23. When you plot them on the x-axis they are close to which integer values?